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\[\Huge \sqrt{\frac{1-x}{1+x}}\]

up to power x^2

i get \[1-x+\frac{x^2}{2} - \frac{x^3}{8} - \frac{3x^4}{64}\]

@saifoo.khan

wolfram got \[-\frac{3 x^5}{8}+\frac{3 x^4}{8}-\frac{x^3}{2}+\frac{x^2}{2}-x+1\]

Unfortunately i forgot the formula! D:

Is it a maclaurin series?

you can try that

I want to know what is meant by Expand, since that's the only thing that comes to mind.

or
\[(1+x)^n = 1+nx+\frac{(n)(n-1)}{2!}(x^2)+...\]

That works for \(n\in \mathbb{N}\).

In this case you have a square root...

still can, watch

expand separately

mix them by multiplying together

Yeah, my problem is with \(1/2 \notin \mathbb{N}\)

I don't think it should be natural number

i mean real number will do

How can you have summations or binomial coefficients with rational numbers?

interval of x is ?

the formula list says can use

we use the second one (1+x)^n

http://en.wikipedia.org/wiki/Binomial_series
look at the History section

|dw:1359798673882:dw|

|dw:1359798819059:dw|

or maybe its \[-\frac{3 x^5}{8}+\frac{3 x^4}{8}-\frac{x^3}{2}+\frac{x^2}{2}-x+1\]

hmm

based from the formula as long as its in the from ("1"+x)^n should be fine to expand, i tried it